Search results
Results from the WOW.Com Content Network
William Feller, in 1949, used the names "forward equation" and "backward equation" for his more general version of the Kolmogorov's pair, in both jump and diffusion processes. [1] Much later, in 1956, he referred to the equations for the jump process as "Kolmogorov forward equations" and "Kolmogorov backward equations". [3]
The forward–backward algorithm runs with time complexity () in space (), where is the length of the time sequence and is the number of symbols in the state alphabet. [1] The algorithm can also run in constant space with time complexity O ( S 2 T 2 ) {\displaystyle O(S^{2}T^{2})} by recomputing values at each step. [ 2 ]
The general algorithm involves message passing and is substantially similar to the belief propagation algorithm (which is the generalization of the forward-backward algorithm). With an algorithm called iterative Viterbi decoding, one can find the subsequence of an observation that matches best (on average) to a given hidden Markov model.
The analysis of errors computed using the global positioning system is important for understanding how GPS works, and for knowing what magnitude errors should be expected. The Global Positioning System makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected.
The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931. [1]
The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time, given the history of evidence. The process is also known as filtering. The forward algorithm is closely related to, but distinct from, the Viterbi algorithm.
Turbo coding is an iterated soft-decoding scheme that combines two or more relatively simple convolutional codes and an interleaver to produce a block code that can perform to within a fraction of a decibel of the Shannon limit.
Reverse accumulation is more efficient than forward accumulation for functions f : R n → R m with n ≫ m as only m sweeps are necessary, compared to n sweeps for forward accumulation. Backpropagation of errors in multilayer perceptrons, a technique used in machine learning , is a special case of reverse accumulation.